Basic limit at infinity question
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Basic limit at infinity question

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
It has to be negative.You can factor whats under the radical as 4(x^2-11)^2, so this reduces to 2(x^2 - 11)/(1-x^2) from that you can get 2(1 - 11/x^2) / (1/x^2 -1).Even without factoring 4x^4 -88x +484, you can multiply it by (1/x^4) and the denominator by (1/x^2) and get √(4 - a - b) / (c -1) where a, b and c are terms that go to 0,......
I keep trying this and getting the same wrong answer:

lim √(4x^4 -88x +484) / (1-x^2)
x-->(-) infinity

The correct answer is -2 but I keep coming up with 2. Can anyone show me a step by step on how to correctly solve this? I have been dividing by the biggest degree in the denominator, then simiplifying the square root.

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Lots of ways to do this. First, notice that for big n, numerator is positive and denominator is negative, so 2 can 't be the answer. It has to be negative.

You can factor what's under the radical as 4(x^2-11)^2, so this reduces to 2(x^2 - 11)/(1-x^2) from that you can get 2(1 - 11/x^2) / (1/x^2 -1). Take out terms going to zero to get 2/(-1) = -2

Even without factoring 4x^4 -88x +484, you can multiply it by (1/x^4) and the denominator by (1/x^2) and get √(4 - a - b) / (c -1) where a, b and c are terms that go to 0, and again you get 2/-1
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